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ATOMS : Make Matrix details

# Make Matrix

A collection of test matrices.
(2352 downloads for this version - 64282 downloads for all versions)
Details
Version
0.4
A more recent valid version exists: 0.5
Author
Michael Baudin
Owner Organization
Consortium Scilab - DIGITEO
Maintainers
Michael BAUDIN
Allan CORNET
Category
License
Dependencies
Creation Date
December 15, 2011
Source created on
Scilab 5.2.x
Binaries available on
Scilab 5.2.x:
Windows 64-bit Windows 32-bit Linux 64-bit Linux 32-bit macOS
Install command
`--> atomsInstall("makematrix")`
Report a bug
Description
```            The goal of this toolbox is to provide a collection of
test matrices.

Some of these matrices appears in specific applied mathematics problems. For
example, the Van Der Monde matrix appears in polynomial interpolation. Another
example is the Hilbert matrix, which arises in the least squares approximation
of arbitrary functions by polynomials.

These test matrices can also be used to experiment with linear algebra
algorithms, such as the resolution of systems of linear equations or the
eigenvalue problem.

For some of these test matrices, the exact eigenvalues, condition number or
invert is known. For example, the Hilbert matrix is symetric positive definite.
Another example is Frank's matrix, which has a unit derminant, but is
ill-conditionned.

Features
-------

* makematrix_border : Returns the Border matrix
* makematrix_cauchy : Returns the Cauchy matrix
* makematrix_circul : Returns the circular matrix
* makematrix_diagonali : Returns a diagonal i matrix
* makematrix_dingdong : Returns the Ding Dong matrix
* makematrix_frank : Returns the Frank matrix
* makematrix_frankmin : Returns the Frank-min matrix
* makematrix_gallery : Returns a test matrix
* makematrix_hadamard : Returns the Hadamard matrix
* makematrix_hankel : Returns the Hankel matrix
* makematrix_hilbert : Returns the Hilbert matrix
* makematrix_invhilbert : Returns the inverse of the Hilbert matrix
* makematrix_magic : Returns the magic matrix
* makematrix_moler : Returns the Moler matrix
* makematrix_normal : Returns a standard normal random matrix
* makematrix_pascal : Returns the Pascal matrix
* makematrix_rosser : Returns the Rosser matrix
* makematrix_toeplitz : Returns the Toeplitz matrix
* makematrix_vandermonde : Returns the Vandermonde matrix
* makematrix_wilkinsonm : Returns the Wilkinson - matrix
* makematrix_wilkinsonp : Returns the Wilkinson + matrix

Demos
-----

* Vandermonde : Interpolation
* Hilbert : Least Squares
* Backslash Test
```
Files (2)
[92.08 kB]
Source code archive
```
```
[120.76 kB]
OS-independent binary for Scilab 5.2.x
```Binary version
Automatically generated by the ATOMS compilation chain

```
News (0)
Comments (2)
Comment -- January 3, 2012, 09:12:56 PM
```This version is correctly packaged.

This test was done with Scilab 5.3.3 on Windows XP 32 bits.

-->atomsTest("makematrix")
TMPDIR = C:\DOCUME~1\Root\LOCALS~1\Temp\SCI_TMP_3860_

001/020 - [SCI\contrib\makematrix\0.4-1] border.................passed
002/020 - [SCI\contrib\makematrix\0.4-1] cauchy.................passed
003/020 - [SCI\contrib\makematrix\0.4-1] circul.................passed
004/020 - [SCI\contrib\makematrix\0.4-1] diagonali..............passed
005/020 - [SCI\contrib\makematrix\0.4-1] dingdong...............passed
006/020 - [SCI\contrib\makematrix\0.4-1] frank..................passed
007/020 - [SCI\contrib\makematrix\0.4-1] frankmin...............passed
008/020 - [SCI\contrib\makematrix\0.4-1] gallery................passed
009/020 - [SCI\contrib\makematrix\0.4-1] hadamard...............passed
010/020 - [SCI\contrib\makematrix\0.4-1] hankel.................passed
011/020 - [SCI\contrib\makematrix\0.4-1] hilbert................passed
012/020 - [SCI\contrib\makematrix\0.4-1] invhilbert.............passed
013/020 - [SCI\contrib\makematrix\0.4-1] moler..................passed
014/020 - [SCI\contrib\makematrix\0.4-1] normal.................passed
015/020 - [SCI\contrib\makematrix\0.4-1] pascal.................passed
016/020 - [SCI\contrib\makematrix\0.4-1] rosser.................passed
017/020 - [SCI\contrib\makematrix\0.4-1] toeplitz...............passed
018/020 - [SCI\contrib\makematrix\0.4-1] vandermonde............passed
019/020 - [SCI\contrib\makematrix\0.4-1] wilkinsonm.............passed
020/020 - [SCI\contrib\makematrix\0.4-1] wilkinsonp.............passed
```
Comment -- January 20, 2012, 10:25:57 PM
```Here is the changelog of v0.4.

makematrix (0.4)
* Updated .start script
* Used assert in the unit tests.
* Removed makematrix_urandom (duplicate with rand)
* Removed makematrix_zeros (duplicate with zeros)
* Removed makematrix_ones (duplicate with ones)
* Removed magic (duplicate with makematrix_magic)
* Removed hadamard (duplicate with makematrix_hadamard)
* Vectorized makematrix_hilbert to increase performances
* Removed rosser (duplicate with makematrix_rosser)
* Improved makematrix_pascal based on specfun_pascal
* Vectorized makematrix_dingdong to increase performances
* Formatted the comments to generate help from the macros.
* Reversed columns of makematrix_vandermonde.
To get the old column order, replace

A = makematrix_vandermonde ( x )

with

A = makematrix_vandermonde ( x );
n = size(A,"c");
A = A(:,n:-1:1);

* Removed wilkinson (duplicate with makematrix_wilkinsonp)
* Vectorized makematrix_vandermonde for increased performances.
* Vectorized makematrix_cauchy for increased performances.
* Generated help from the sources.
* Renamed gallery into makematrix_gallery for consistency.
* Vectorized makematrix_frankmin for increased performances.
* Created Vandermonde Interpolation demo.
* Created Hilbert Least Squares demo.
* Vectorized makematrix_border for increased performances.
* Vectorized makematrix_moler for increased performances.
* Used apifun to check arguments.
```
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